DSpace Collection:
http://hdl.handle.net/10174/995
2019-07-15T22:00:14ZGeneral constitutive updating for finite strain formulations based on assumed strains and the Jacobian
http://hdl.handle.net/10174/25509
Title: General constitutive updating for finite strain formulations based on assumed strains and the Jacobian
Authors: P, Areias
Abstract: Compatibility between element technology featuring assumed (finite)-strains based on least-squares and current constitutive formulations employed in elastic and inelastic contexts is a demanding task. Local frames are required for anisotropic and cohesive laws, some assumed-strain element technologies do not explicitly provide the deformation gradient, and total Lagrangian approaches are often inadequate for advanced plasticity models. Kirchhoff stress-based Fe Fp decompositions are also not convenient for ductile damage models. In addition, if rotational degrees-of-freedom are used, as is the case in beams and shells, the adoption of a fixed undeformed configuration causes implementation brittleness. An additional aspect to consider is remeshing by element partitioning, which precludes the storage of constitutive tensors in local frames, invalidating the stored quantities. Based on seven algorithmic requirements and the corresponding design solutions, we introduce a general constitutive updating algorithm based on the strain and the Jacobian provided by the element. This allows the use of virtually any constitutive law with any finite-strain element formulation while satisfying the seven requirements. In addition, Newton-Raphson convergence properties are extraordinary, at the cost of precision in the strain rate estimation. As a prototype element implementation, we present a stable hexahedron based on least-squares strains. A BFGS secant estimation is employed for the weight in the least-squares so that softening constitutive laws can be adopted without stability issues at the element level.2018-01-01T00:00:00ZEffective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation
http://hdl.handle.net/10174/25506
Title: Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation
Authors: Areias, P; Reinoso, J.; Camanho, P; César de Sá, J; Rabczuk, T
Abstract: In this paper, we propose a simple 2D and 3D crack evolution algorithm which avoids the variable/DOF mapping within mesh adaptation algorithms. To this end, a new area/volume minimization algorithm for damaged elements is introduced with the goal of improving the crack path representation. In addition, the new algorithm consists of: (i) mesh-creation stage where a damage model is employed to drive the remeshing procedure (ii) a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation. This is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered algorithm for equilibrium and screened Poisson equations is used in this second stage. Element subdivision is based on edge split operations in 2D and 3D using the damage variable. Both 2D and 3D operations are described in detail. With the objective of assessing the robustness and accuracy of the algorithm, we test its capabilities by means of four quasi-brittle benchmark applications.2018-01-01T00:00:00ZFully-coupled piezoelectric assumed-strain least-squares nonlinear shell
http://hdl.handle.net/10174/25498
Title: Fully-coupled piezoelectric assumed-strain least-squares nonlinear shell
Authors: Areias, P; Rabczuk, T; César de Sá, J; Mota Soares, C
Abstract: Relevance of finite strain shell piezoelectric analysis is significant due to the general use of polyvinylidene fluoride (PVDF). A finite-strain geometrically exact shell model for the analysis of piezoelectric laminated structures is introduced. An assumed-strain formulation is employed, with least-squares fitting of contravariant linear stress fields. This allows the condensation of internal degrees-of-freedom corresponding to the assumed strains. The resulting piezoelectric shell has 8 degrees-of-freedom in each node, with 3 position/displacement degrees-of-freedom, 3 rotation parameters and the upper and lower electrostatic potential at the nodes. This contrasts with available formulations where only one electric degree-of-freedom is considered. A total of 32 degrees-of-freedom in each 4-node element are used. In term of implementation, we use a generalized strain and generalized stress formulation to reproduce the conventional finite element organization. Six examples are presented, with transversely isotropic and orthotropic cases, including finite strains and asymmetric plies. Results show a remarkably good agreement with the sources and we achieve higher values of actuation.2018-01-01T00:00:00ZQuark Mass Functions and Pion Structure in the Covariant Spectator Theory
http://hdl.handle.net/10174/25021
Title: Quark Mass Functions and Pion Structure in the Covariant Spectator Theory
Authors: Biernat, Elmar P.; Gross, Franz; Peña, Teresa; Stadler, Alfred; Leitão, Sofia
Abstract: The Covariant Spectator Theory is applied to the description of quarks and the pion. The dressed quark mass function is calculated dynamically in Minkowski space and used in the calculation of the pion electromagnetic form factor. The effects of the mass function on the pion form factor and the different quark-pole contributions to the triangle diagram are analyzed.2018-08-31T23:00:00Z